Abstract : The BICEP2 collaboration reported recently a B-mode polarization of the cosmic microwave background CMB radiation inconsistent with the null hypothesis at a significance of > 5 sigma. This result has been often interpreted as a signature of primordial gravitational waves from cosmic inflation, even if actually polarized dust emission may be at the origin of such a signal. Even assuming that part of this CMB B-mode polarization really corresponds to the early Universe dynamics, its interpretation in terms of inflation and primordial gravitational waves is not the only possible one. Alternative cosmologies such as pre-Big Bang patterns and the spinorial space-time SST we introduced in 1996-97 can naturally account for such CMB B-modes. In particular, the SST automatically generates a privileged space direction PSD whose existence may have been confirmed by Planck data. If such a PSD exists, it seems normal to infer that vector perturbations have been present in the early Universe leading to CMB B-modes in suitable cosmological patterns. Inflation would not be required to explain the BICEP2 result assuming it really contains a primordial signal. More generally, pre-Big Bang cosmologies can also generate gravitational waves in the early Universe without any need for cosmic inflation. We further discuss here possible alternatives to the inflationary interpretation of a primordial B-mode polarization of cosmic microwave background radiation.